C2 chapter 3 - exponentials and logarithms

This chapter introduces exponential functions and their inverses: logarithms.

C2 section 3.1 exponential functions

Before you start here, you should have a good recall and understanding of the use of indices to express powers and you need to know the laws of logarithms. You can revise this by reviewing C1 chapter 1 - algebra and functions, especially sections 1.2 and 1.6
By the end of this section, you will have evaluated exponential functions such as y = 2x and similar functions. You will be able to identify key points on the graphs of such functions and anticipate the effect of changing the base value a in y = ax.

Examples:
Starter puzzle - suppose you have a choice of two different jobs at graduation:

• A starting salary of £20,000 p.a. with a 6% per year increase

or

• A starting salary of £24,000 p.a. with a £1000 per year raise

Which should you choose?
Why?
When will one 'overtake' the other?


Mr Liu's introductory presentation to exponential functions:

C2 section 3.6 - changing the base of logarithms

We need to be able to change the base of logarithms using the formula
$\displaystyle \log_a{x} = \dfrac{\log_b{x}}{\log_b{a}}$


(there's a typo at around 7:09 where I put y² -5x +4 = 0 not y² -5y +4 = 0. I'll re-record that later.)

C2 Exercise 3F